In a way, I'm more worried about the size and shape of the travel box for my plane(s) and etc.

Years ago I visited my buddy in AK and wanted to take a plane with me too. I was pretty new and had a T-28 Parkzone Foamy. I built a wooden box that allow the fuse with the wing separated to fit inside. I then simply checked it as baggage. Everything turned out just fine. As I recall there was no extra charge but things may have changed now. We had a blast flying.